Department of Mathematical Sciences
Colloquia and Seminars
Areas of Research
About the Department
- Putnam Mathematical CompetitionThe William Lowell Putnam Mathematical Competition is an annual
contest for college students established in 1938 in memory of
its namesake. This contest is administered by the Mathematical
Association of America. Over 4000 undergraduate students from
nearly 600 institutions in North America took part in the exam
in 2015. Carnegie Mellon's team, which consisted of Josh Brakensiek, Linus Hamilton, and Thomas Swayze placed second.
This was the fifth top 5 performance in a row for CMU. Furthermore, 41 CMU students placed among the top 470.
- Wes Pegden named Sloan Research FellowWes Pegden, an assistant professor of Mathematical Sciences, was
named a 2016 Sloan Research Fellow. These fellowships seek to
stimulate fundamental research by early-career scientists and
scholars of outstanding promise.
Professor Pegden's research is in the area of combinatorics.
He works on combinatorial games, random structures, and
random instances of computational problems. Pegden and
his coauthors are developing a remarkable account of the scaling limit of the Abelian Sandpile Process and have developed new perspectives
on the hardness of geometric cases of the Traveling Salesman
Problem. Professor Pegden is affiliated with Carnegie Mellon's
interdisciplinary PhD program in Algorithms, Combinatorics and
- Boris Bukh awarded NSF CAREER grantBoris Bukh, an assistant professor of Mathematical Sciences, received
an NSF CAREER Award . The Faculty Early Career Development (CAREER)
Program offers the National Science Foundation's most prestigious awards in support of junior faculty who exemplify the role of
teacher-scholars through outstanding research, excellent education
and the integration of education and research. Professor Bukh was
also named a 2015 Sloan Research Fellow. These fellowships seek to stimulate fundamental research by early-career scientists and
scholars of outstanding promise.
Professor Bukh's research connects combinatorics and geometry with other areas of mathematics. He studies the appearance of rigid geometric structures as answers (or conjectured answers) to classical combinatorial problems, the problem of approximation of large geometric point sets, and geometric incidence problems. His work on these problems draws on tools from - and makes connections with - logic, number theory, and algebraic topology. Professor Bukh is affiliated with Carnegie Mellon's interdisciplinary PhD program in Algorithms, Combinatorics and Optimization.
- Workshop In Honour of the 60th Birthday of Irene FonsecaNew Challenges for the Calculus of Variations Stemming From Problems in the Materials Sciences and Image Processing
CRM, Montreal, Canada, May 16-20, 2016
Organizers: R. Choksi, N. Fusco, C. Larsen and G. Leoni
- PIRE-CNA 2016 Summer SchoolNew Frontiers in Nonlinear Analysis for Materials
Center for Nonlinear Analysis, Carnegie Mellon University, June 2-10, 2016
Organizers: Irene Fonseca, Giovanni Leoni, Stefan Müller, Christoph Ortner
- Conference in honor of David Kinderlehrer's 75th birthdayTopics in Applied Nonlinear Analysis: Recent Advances and New Trends
Carnegie Mellon University, July 18-20, 2016
Organizers: Maria Emelianenko, Yekaterina Epshteyn, Irene Fonseca, Michał Kowalczyk, Chun Liu, Pablo Pedregal, Dejan Slepčev, Adrian Tudorascu
- Bob Pego named AMS FellowThe Fellows of the American Mathematical Society program
recognizes mathematicians who have made outstanding
contributions to the creation, exposition, advancement,
communication, and utilization of mathematics. Bob Pego
was recently named an AMS Fellow for contributions to
partial differential equations and applied mathematics.
His research concerns dynamical behavior in
nonlinear partial differential equations that model a
wide range of phenoma including incompressible fluid
flow, water waves, and coagulation dynamics. Professor
Pego joins CMU Department of Mathematical Sciences
faculty Irene Fonseca, Alan Frieze and David Kinderlehrer
among the ranks of AMS Fellows.
- Master of Science in Computational Finance ranked #1QuantNet, a leading online resource for the fields of
financial engineering and quantitative finance, has
recognized the Master in Computational Finance (MSCF) program at Carnegie Mellon University as #1 in its
2015 ranking of financial engineering programs.
This is the third #1 ranking in a row for MSCF.
"Quantitative finance offers students with superior
math skills an opportunity to work in an intellectually
challenging environment, using their skills in an
industry on which the economic health of our nation
depends," said Steve Shreve, University Professor of
Mathematical Sciences and one of the founders of the
CMU MSCF program. "Recognizing this, Carnegie Mellon
created the first professional degree in quantitative
finance more than 20 years ago, and we have invested substantial resources toward the goal of making ours the best quantitative
finance degree in the world. It is gratifying to see
that even though scores of similar programs have since been created at many other elite universities,
our number one standing continues."
The Department of Mathematical Sciences plays a
critical role in the inter-disciplinary MSCF program, teaching a third of the curriculum and providing
leadership in policy matters. The Department is
deeply invested in the applications of mathematics
to finance. The Department is home to the Bachelor's
program in Computational Finance and graduates a
steady stream of Ph.D. students whose research treats
mathematical problems arising in finance.
- Alumnus John NashThe Department of Mathematical Sciences extends its deepest sympathies to the family of alumnus John F. Nash, Jr., who died along with his wife in a car accident on Saturday, May 23. John Nash's death came less than a week after he received the 2015 Abel
The Norwegian Academy of Sciences and Letters awarded the Abel
Prize for 2015 to John F. Nash, Jr. and Louis Nirenberg “for
striking and seminal contributions to the theory of nonlinear
partial differential equations and its applications to
geometric analysis.” While the Fields medal is considered the highest honor in
mathematics, the Fields medal is restricted to mathematicians
under the age of 40. The Abel prize, considered the equivalent
of a Noble Prize, is the most important prize honoring
contributions to mathematics over the course of a career.
John Nash received bachelor and masters degrees in mathematics
from Carnegie Tech in 1948. He went on to complete his Ph.D.
at Princeton and to make seminal contributions in a number of
areas. Nash was awarded the Nobel prize in economics in 1994
for his work on non-cooperative games. The work on game theory
is distinct from the work on partial differential equations
and geometric analysis that was recognized by the Abel
- Putnam Mathematical CompetitionCMU team places 5th on the 2014 William Lowell Putnam Mathematical Competition. This is the fourth top 5 Putnam performance in a row
for CMU. Furthermore 55 CMU students placed in the top 507.
- Po-Shen Loh wins NSF CAREER AwardPo-Shen Loh, an assistant professor of Mathematical
Sciences, received an NSF CAREER Award. The Faculty
Early Career Development (CAREER) Program offers the
National Science Foundation's most prestigious awards
in support of junior faculty who exemplify the role
of teacher-scholars through outstanding research,
excellent education and the integration of education
and research within the context of the mission of
Professor Loh's research lies at the intersection of
combinatorics and probability theory. He uses
randomness as a component in the construction of
discrete mathematical objects and also introduces
randomness as a proof technique to solve problems
about purely deterministic systems. Some of
Professor Loh's work is motivated by problems from
computer science. He is affiliated with Carnegie
Mellon's interdisciplinary PhD program in
Algorithms, Combinatorics and Optimization and has
developed an innovative problem-solving seminar
series for undergraduate students, inspired by the
annual Putnam exam.
- Alan Frieze delivered plenary lectureProfessor Alan Frieze delivered a plenary lecture at the 2014
International Congress of Mathematicians (ICM). The
ICM is one of the largest and most prestigious
international congresses in the mathematics community.
A number of major prizes, including the Fields Medal,
are awarded at this event. As the ICM is held once
every four years, only a very select group of
mathematicians who have had a major
impact on the field are invited to deliver plenary
Professor Frieze is a pioneer in the study of random
combinatorial structures and the use of randomness in
algorithms. His polynomial-time algorithm for
approximating the volume of a convex body (joint work
with M. Dyer and R. Kannan) has had a lasting impact on theoretical Computer Science.
Another major contribution (also in joint work with
R. Kannan) is a weak version of the Szemeredi
Regularity Lemma. This weak regularity Lemma is
a critical tool in Combinatorics.
- David Kinderlehrer named SIAM FellowThe SIAM Fellows Program honors mathematicians who are recognized by their peers as distinguished for their
contributions to the discipline. David Kinderlehrer
was recently named a SIAM Fellow in recognition of his
contributions to nonlinear partial differential
equations, the calculus of variations, and mathematical aspects of materials science. Professor Kinderlehrer
joins CMU Department of Mathematical Sciences faculty
Irene Fonseca, Alan Frieze and Bob Pego among the ranks
of SIAM Fellows.
- Po-Shen Loh appointed National Lead Coach for the USA International Mathematical Olympiad TeamThe International Mathematical Olympiad is the premier math competition for
high school students worldwide, and is the oldest of the International
Science Olympiads. Since its inception in 1959, the Olympiad has developed
a rich legacy, facilitating early talent identification and cultivation on
nationwide scales. Each country independently organizes its own Olympiad
program, and Po-Shen Loh, Assistant Professor of Mathematics and CMU's
Putnam organizer, has been appointed to the national lead coach position
("Team Leader") for the United States of America. In addition to directing
national team selection and training activities, Po-Shen is building upon
the Olympiad platform to bridge the worlds of high school and research
mathematics, as well as to broaden interest in mathematics on the national
- Putnam Mathematical CompetitionCMU team places 2nd on the 2013 William
Lowell Putnam Mathematical Competition. This is
the third top 5 Putnam performance in a row for CMU.
- Master of Science in Computational Finance ranked #1 QuantNet, a leading online news outlet in the field of financial engineering,
has recognized the Master in Computational Finance (MSCF) program at Carnegie
Mellon University as #1 in its 2013 ranking of financial engineering programs.
This is the second #1 ranking in a row for MSCF, which was also ranked first
in the 2011 Quantnet ranking.
"We created the first professional degree in computational finance
almost 20 years ago, and now there are scores of them, including
at Columbia, NYU, Princeton and UC-Berkeley," said Steve Shreve, Professor
of Mathematical Sciences and one of the founders of the CMU MSCF program.
"I believe we owe our leading position to the fact that Mathematical
Sciences chose to create this degree jointly with the Tepper School of
Business, the Department of Statistics, and the information technology
faculty in the Heinz College. To succeed in the finance industry, one
needs a strong foundation in math, but one also needs to deal with data,
write computer code, and understand the business environment.
Inter-disciplinarity is a hallmark of Carnegie Mellon."
Although MSCF is inter-disciplinary, the Department of Mathematical Sciences plays a critical role, teaching a third of the curriculum and providing leadership in policy matters. The Department is deeply invested in the applications of mathematics to finance. The Department is home
to the Bachelor's program in Computational Finance and graduates a steady stream of Ph.D. students whose research treats mathematical problems arising in finance.
- Mackey wins the 2013 Ryan teaching awardJohn Mackey, Teaching Professor, Associate Department Head and Director of Undergraduate Studies in Mathematical Sciences, received the
2013 William H. and Frances S. Ryan Award for Meritorious Teaching.
This prestigious university-wide award is given annually to
a faculty member at Carnegie Mellon who has demonstrated
unusual devotion and effectiveness in teaching. Professor
Mackey is particularly adept at delivering sophisticated
mathematical content to large groups of students. This is apparent
in his extremely successful re-design of the
course Concepts of Mathematics, a course that plays a pivotal role in
the Mathematics and Computer Science curricula at CMU.
- Putnam Mathematical CompetitionCMU team places 5th on the 2012 William Lowell Putnam Mathematical Competition. This is the fifth top 5 Putnam performance for CMU.
- Gautam Iyer Awarded Sloan FellowshipGautam Iyer, an assistant professor of Mathematical Sciences and
member of the Center for Nonlinear Analysis, was named a 2013 Sloan Research
Fellow . These fellowships seek to stimulate fundamental research by
early-career scientists and scholars of outstanding promise. Iyer also received an NSF CAREER Award in 2013. The Faculty Early Career Development (CAREER) Program offers the National Science Foundation's most prestigious awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research.
Professor Iyer studies the equations that model incompressible fluids,
diffusive transport, mixing, liquid crystals and coagulation using tools from
both Probability and Analysis. His research advances our understanding of
mathematical models for a variety of phenomena, including physical and chemical
One of Professor Iyer's research projects addresses vacuums in fluids. It is
universally known that nature abhors a vacuum. In the context of compressible
fluids, however, a rigorous proof of this law has eluded mathematicians for
quite some time. Professor Iyer hopes to use a probabilistic
representation of fluids that he developed in his phd thesis to further our
understanding of the emergence of vacuum states in compressible fluids.
- President of the Society for Industrial and Applied MathematicsPITTSBURGH— Irene Fonseca, Mellon College of Science Professor of Mathematics, has been elected president of the Society for Industrial and Applied Mathematics, an international professional society for applied mathematicians. She served a one-year term as president-elect in 2012. On January 1, 2013 she began a two-year term as president.